Pith Number

pith:WIKOFCFW

pith:2023:WIKOFCFWHYHRHNVQ3NBQOC6EQY

not attested not anchored not stored refs pending

Theory of gravitational lensing on a curved cosmic string

Igor I. Bulygin, Mikhail V. Sazhin, Olga S. Sazhina

arxiv:2306.09062 v1 · 2023-06-15 · astro-ph.CO · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WIKOFCFWHYHRHNVQ3NBQOC6EQY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T06:21:08.142934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b214e288b63e0f13b6b0db43070bc48613ad96f29a7da4f3977b5952361b6b6e

Aliases

arxiv: 2306.09062 · arxiv_version: 2306.09062v1 · doi: 10.48550/arxiv.2306.09062 · pith_short_12: WIKOFCFWHYHR · pith_short_16: WIKOFCFWHYHRHNVQ · pith_short_8: WIKOFCFW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WIKOFCFWHYHRHNVQ3NBQOC6EQY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b214e288b63e0f13b6b0db43070bc48613ad96f29a7da4f3977b5952361b6b6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7aa7cee9b92793fbd9f69e304c2fe567ffa62004f324212393b39e0a904f20a",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2023-06-15T11:44:54Z",
    "title_canon_sha256": "6c5677d03d0a42c22cfcc99bb479500f8a47c54f1894b2856d73fc1a2db68b90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.09062",
    "kind": "arxiv",
    "version": 1
  }
}